SOLUTION: I really could use some help on this please, Thank you! a) Find all zeros of f(x) b) Write the complete factored form of f(x) Using p/q and synthetic substitution I think?

Algebra ->  Systems-of-equations -> SOLUTION: I really could use some help on this please, Thank you! a) Find all zeros of f(x) b) Write the complete factored form of f(x) Using p/q and synthetic substitution I think?       Log On


   

Question 422980: I really could use some help on this please, Thank you!
a) Find all zeros of f(x)
b) Write the complete factored form of f(x)

Using p/q and synthetic substitution I think? I'm not sure.
Here is the equation.
f(x) = 3x^3 + 3x
Found 3 solutions by Gogonati, jim_thompson5910, richard1234:
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Answer: First we factor the expression, after equalize it with zero:
+3x%5E3%2B3x=3x%2A%28x%5E2%2B1%29
The product +3x%2A%28x%5E2%2B1%29=0+, when 3x=0 or x=0
The factor x%5E2%2B1+ is always positive for every value of x.
The only root for our equation is {0}.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Simply factor out the GCF 3x to get 3x%5E3+%2B+3x=3x%28x%5E2%2B1%29. I'll let you take it from here.


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Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) factors to 3x(x^2 + 1) = 0. Either 3x = 0 or x^2 + 1 = 0 --> x^2 = -1. The only real root is x=0, while x^2 = -1 has two complex roots, i and -i.